Continuous Singularity Free Approach to the Three-Dimensional Bearings-Only Tracking Problem

This work presents a new description of the three-dimensional bearings-only tracking problem. A review of established approaches reveals that the common use of elevation and azimuth angles in the state or the measurement model can cause unrealistic error distributions and is not well suited to Kalman filtering under certain relevant circumstances. It is furthermore shown that such methods immanently corrupt rotational invariance and thus let estimation performance rely on a fortunate choice of the inertial reference system. Based on these considerations, an alternative representation is derived that aims at eliminating the prior identified shortcomings. A corresponding tracking filter is designed and demonstrated to give equivalent or superior performance compared with usual approaches.